Site of the Gleaners who think the universe is a spherical surface in at least four-dimensional space


1. Historical first meeting of the Gleaners: A simple reason why the universe seems to be closed


Glass Snake: Hello! My name as a Gleaner is Glass Snake. Gleaners are those who think the universe is closed. If it is closed, it is a spherical surface. Because the universe has three distance dimensions and one time dimension (distances and time cannot be separated completely from each other by the theory of relativity), it is a spherical surface in (at least) four-dimensional space.

            If you have a feeling that the universe might be closed, even though the feeling is the slightest one, then you are a member of the Gleaners.


            You might think that the experts have been studying such a subject and we don't need to think about the universe. However, the experts are afraid of damaging their careers, so they dare not announce that the universe is closed. Thus Gleaners need to do the work.


Robot: Yes, you have completely nothing to lose.


Glass Snake: It's none of your business. First of all I'd like to suggest that we call the members of the Gleaners after the Chinese ancient astrological calendar. For example, I was born in 1953 or 1965(the snake year in the calendar) and I wear glasses for near sight, so my name is Glass Snake, i.e. G. Snake.


Puzzle Sheep: Hi! My name as a Gleaner is Puzzle Sheep. For I was born in 1955, 1967, or 1979(the sheep year) and I enjoy solving number puzzles.


Stamp Pony: How are you? I was born in 1990(the horse year) and my hobby is collecting used stamps, so I'm Stamp Pony.


Robot: Good afternoon, every android! I'm an assistant robot. I was manufactured in 2006(the dog year) and I prefer machine oil to electricity. I regenerate wearing machine oil No. 5 every night, so if you could call me Oil Doberman.


All: A very fascinating name!


Glass Snake: O. K. Then c, Robot, name the subject of this meeting.


Robot: Logic doesn't care as Gene Roddenberry said. Dr. Shiraishi programmed me less emotional than HAL 9000 used in the movie e2001: A Space Odysseyf.

            The subject of this meeting is to discuss the reason why the universe seems to be closed.


Glass Snake: A very direct and simple reason is that the density of stars, those observed in the night sky on the earth, is almost completely uniform in all directions (isotropic). If the universe is open as shown in Fig. 1, then since it is naturally supposed that the earth is not at the center of the universe, the density of stars in direction D12 is more dens than that in direction D11. But the density is uniform, so the universe is closed as shown in Fig. 2. Since the closed universe is the surface S of a sphere in a three-dimensional representation, the density of stars in all directions including directions D21, D22, and D23 are almost the same.



Puzzle Sheep: Is that all?


Stamp Pony: As humans have been watching stars in the night sky for a very long time, it seems to me that they haven't paid much attention to the isotropic nature of the star density.


Glass Snake: But, if we suppose that the universe is open, how do you explain on the isotropic nature?


Puzzle Sheep: It will be possible to explain why the density is isotropic using some open universe model, but we have to create a very complicated theory like the geocentric theory, i.e. Ptolemaic theory.


Stamp Pony: If we have created such a theory, we will have to amend the theory each time when a contradiction between the theory and the observation is discovered.


Robot: Our theory is as simple as the heliocentric theory, i.e. Copernican theory.


Glass Snake: Using the supposition that the universe is closed, as will be shown in the following meetings, we can understand why the cosmic microwave background (CMB) is so isotropic, and we may possibly deny the acceleration of the expansion speed of the universe. I hope these discussions will help other people support our theory.


            Although the universe is (at least) four dimensional, the conventional world that we can observe is three dimensional, and a projection of a spherical surface in a four-dimensional space into the conventional world is a sphere.

Stamp Pony: It seems to me that whether the universe is closed doesnft concern our everyday life at all.

Glass Snake:
On the contrary, the fate of the earth totally depends on our work. What if, tomorrow or some day in the near future a highly advanced alien space ship arrives at an orbit around the earth, and the aliens announce eWe are from the other side of the galaxy, and we shall ask a question to the residents of the earth. If the answer is wrong, we shall destroy the earth. The question is, of course, if the universe is closed or not?f

Puzzle Sheep: I doubt if such a situation will really occur.

Robot: Technically speaking, the possibility is not zero.

Glass Snake: Then if the experts hesitate to answer the question, it is the Gleaners who will advise the leaders of the earth to answer that the universe is closed. Then the alien ship will leave the orbit and go to the next earth-like planet. As a result the earth will be saved.

Stamp Pony: By the way do you know the leaders of the earth?

Glass Snake: Of course I know the leaders.

Robot: And in my knowledge the leaders donft know G. Snake at all.

Glass Snake: Anyway the important thing is to recognize the universe as correctly as possible.

             Further, it should be noted that when we want to study the paths of rays of light on a spherical surface in a four-dimensional space, it suffices for us only to study the paths of rays of light on a spherical surface in the conventional world. This will be understood by the fact that a projection of a spherical surface in the conventional (three-dimensional) world into a two-dimensional world is a circle, and the paths of rays of light on the spherical surface are those which can be obtained by rotation of a circumference.


Robot: I shall ask you to close the first meeting now.


All: We are those who live on a spherical surface, that is, we are spherical-surfacelings!

            We are the Gleaners!


Robot: In Russian accent!


All: Allo, we are Gleaners!


Robot: In Japanese accent!


All: Gokigenyo, we are the Greeners!


Robot: You, self-righteous spherical-surfacelings! Dismissed!


A narrow and maybe insecure path to the Gleaners:

(Mail to:


2. Historical second meeting of the Gleaners

(A reason why the cosmic microwave background (CMB) is so isotropic)


3. Historical third meeting of the Gleaners

(The expansion speed of the universe is probably not accelerated)

4. Historical fourth meeting of the Gleaners

(A direct method of confirming that the universe is closed, but c)

5. Historical maybe last meeting of the Gleaners

(The Doppler shift pattern in the closed universe ---

It might have been proved already)

6. A mathematical formulation of the closed universe model (Appendix)

7. An explanation on the variation of the Hubble constant (A spin-off meeting)